Title:The Predicted Metallicity Distribution of Stars in Dwarf Spheroidal Galaxies

Abstract: We predict the metallicity distribution of stars and the age-metallicity relation for 6 Dwarf Spheroidal (dSph) galaxies of the Local Group by means of a chemical evolution model which is able to reproduce several observed abundance ratios and the present day total mass and gas content of these galaxies. The model adopts up to date nucleosynthesis and takes into account the role played by supernovae of different types (II, Ia) allowing us to follow in detail the evolution of several chemical elements (H, D, He, C, N, O, Mg, Si, S, Ca, and Fe). Each galaxy model is specified by the prescriptions of the star formation rate and by the galactic wind efficiency chosen to reproduce the main features of these galaxies. These quantities are constrained by the star formation histories of the galaxies as inferred by the observed color-magnitude diagrams (CMD). The main conclusions are: i) 5 of the 6 dSphs galaxies are characterized by very low star formation efficiencies ($\nu = 0.005 - 0.5 Gyr ^{-1}$) with only Sagittarius having a higher one ($\nu = 1.0 - 5.0 Gyr ^{-1}$); ii) the wind efficiency is high for all galaxies, in the range $w_i$ = 6 - 15; iii) a high wind efficiency is required in order to reproduce the abundance ratios and the present day gas mass of the galaxies; iv) the predicted age-metallicity relation implies that the stars of the dSphs reach solar metallicities in a time-scale of the order of 2 - 6 Gyr; v) the metallicity distributions of stars in dSphs exhibit a peak around [Fe/H] $\sim$ -1.8 to -1.5 dex, with the exception of Sagittarius ([Fe/H] $\sim$ -0.8 dex); iv) the predicted metallicity distributions of stars suggest that the majority of stars in dSphs are formed in a range of metallicity in agreement with the one of the observed stars.